Shifts in Cayley graphs |
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Authors: | Gabriel Verret |
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Affiliation: | Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | An automorphism of an undirected simple graph is called a shift if it maps every vertex to an adjacent one. For all finite groups G, we determine the minimum nonzero valency of a Cayley graph on G that does not admit a shift. We also get a classification of groups with all involutions central and such that for every pair a,b of elements of the group, one of ab=ba, aba−1=b−1, bab−1=a−1 or a2=b±2 holds. |
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Keywords: | Cayley graph Shift Mobility |
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